Overview representation of Bsplines curves and surfaces

Abstract

Having curve and surface are extremely important in generating a realistic object in virtual environment. Curve and surface are normally represented by B-Spline and Bezeir. However, B-splines have two advantages over Bezier splines : (1) the degree of a B-spline polynomial can be set independently of the number of control points (with certain limitations), and (2) B-splines allow local control over the shape of a spline curve or surface. The trade-off is that B-splines are more complex than Bezier splines. Bézier basis functions are used as weights. B-spline basis functions will be used the same way; however, they are much more complex. There are two interesting properties that are not part of the Bézier basis functions, namely: (1) the domain is subdivided by knots, and (2) basis functions are not non-zero on the entire interval. In fact, each B-spline basis function is non-zero on a few adjacent subintervals and, as a result, B-spline basis functions are quite "local".